Special Triangles

Find the missing side lengths. Leave answers as radicals in the simplest form.

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = and tan30° = , then

cos30° = = = ( cross- multiply )

× m = 12 ( divide both sides by )

m = ← rationalise by multiplying numerator/ denominator by )

m = × = = 4

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tan30° = = = ( cross- multiply )

× n = 6 ( divide both sides by )

n = ← rationalise the denominator

n = × = = 2

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step-by-step explanati∵∵∴∴on:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet